Yes: check the syntax (however strict you want to be), double check that the domain has an A/MX record (having an MX is typical but not required), and if you're still having huge bounce rates (likely won't) then you can worry about trying to validate recipients.

If you get a bounce then you can reasonably conclude that the recipient does not exist. Anything less and you can't really be sure whether they exist or not because what happens is entirely up to the remote mail server; maybe the email will be rejected because the mail server doesn't like you, or maybe it will be silently rejected, or maybe it will be delivered to a catch-all account, or maybe it'll make it to an actual inbox and human eyes.

This is getting beyond the scope of this thread, and the entire PHP forum really, but yes: using a double opt-in (aka sending a verification email) helps. Clear unsubscribe links, sender verification measures, all those other nice things are good too because bounce rates and spam filters are directly related to each other. But even if you do everything possible you won't get 100%, so instead your goal should be keeping up to date on mailing list and anti-spam best practices.

I was using Briteverify for a while, then i recently found Zerobounce email validation system. They are both excellent validation systems, but Zerobounce provides a lot more information that useful to me so I switch, not to mention they are cheaper.

There are issues with briteverify like it is not able to check if the email address is a catchall email account or not and it just mark it as just valid. If you are looking for a better service then there are other great Bulk Email Verifier you should consider as they provide better results.